P. [178]. Idealism of Philosophy: cf. Schelling, ii. 67. 'Every philosophy therefore is and remains Idealism; and it is only under itself that it embraces realism and idealism; only that the former Idealism should not be confused with the latter, which is of a merely relative kind.'
Hegel, Werke, iii. 163. 'The proposition that the finite is "ideal" constitutes Idealism. In nothing else consists the Idealism of philosophy than in recognising that the finite has no genuine being.... The contrast of idealistic and realistic philosophy is therefore of no importance. A philosophy that attributed to finite existences as such a genuine ultimate absolute being would not deserve the name philosophy.... By "ideal" is meant existing as a representation in consciousness: whatever is in a mental concept, idea or imagination is "ideal": "ideal" is just another word for "in imagination,"—something not merely distinct from the real, but essentially not real. The mind indeed is the great idealist: in the sensation, representation, thought of the mind the fact has not what is called real existence; in the simplicity of the Ego such external being is only suppressed, existing for me, and "ideally" in me. This subjective idealism refers only to the representational form, by which an import is mine.'
P. [180], § 96. The distinction of nature and mind as real and ideal is especially Schelling's: See e.g. his Einleitung, &c. iii. 272. 'If it is the problem of Transcendental Philosophy to subordinate the real to the ideal, it is on the contrary the problem of the philosophy of nature to explain the ideal from the real.'
P. 183, § 98. Newton: see Scholium at the end of the Principia, and cf. Optics, iii. qu. 28.
Modern Atomism, besides the conception of particles or molecules, has that of mathematical centres of force.
Kant, Werke, v. 379 (ed. Rosenk.). 'The general principle of the dynamic of material nature is that all reality in the objects of the external senses must be regarded as moving force: whereby accordingly so-called solid or absolute impenetrability is banished from natural science as a meaningless concept, and repellent force put in its stead; whereas true and immediate attraction is defended against all the subtleties of a self-misconceiving metaphysic and declared to be a fundamental force necessary for the very possibility of the concept of matter.'
P. [184], § 98. Abraham Gottheit Kästner (1719-1800), professor forty-four years at Göttingen, enjoyed in the latter half of the eighteenth century a considerable repute, both in literature and in mathematical science. Some of, his epigrams are still quoted.
P. [190], § 102. The two 'moments' of number Unity, and Sum (Anzahl), may be compared with the Greek distinction between one and ἀριθμός (cf. Arist. Phys. iv. 12 ἐλάχίστος ἀριθμός ἡ δυάς). According to Rosenkranz (Leben Hegels) the classification of arithmetical operations often engaged Hegel's research. Note the relation in Greek between λογικόν and λογιστικόν. Cf. Kant's view of the 'synthesis' in arithmetic.
P. [193], § 103. Intensive magnitude. Cf. Kant, Kritik der reinen Vernunft, p. 207, on Anticipation of Perception (Wahrnehmung), and p. 414, in application to the question of the soul's persistence.
P. [195], § 104. Not Aristotle, but rather Simplicius on the Physics of Aristotle, fol. 306: giving Zeno's argument against the alleged composition of the line from a series of points. What you can say of one supposed small real unit, you can say of a smaller, and so on ad infinitum. (Cf. Burnet's Early Greek Philosophy, p. 329.)